Branched polymers with loops coupled to the critical Ising model
arXiv:2512.24633 · doi:10.1103/qs2c-v9w8
Abstract
We study the continuum limit of branched polymers (BPs) with loops coupled to Ising spins at the zero-temperature critical point. It is known that the continuum partition function can be represented by a Hermitian two-matrix model, and we propose a string field theory whose Dyson-Schwinger equation coincides with the loop equation of this continuum matrix model. By setting the matrix size to one, we analyze a convergent non-perturbative partition function expressed as a two-dimensional integral, and show that it satisfies a third-order linear differential equation. In contrast, in the absence of coupling to the critical Ising model, the continuum partition function of pure BPs with loops is known to satisfy the Airy equation. From the viewpoint of two-dimensional quantum gravity, we introduce a non-perturbative loop amplitude that serves as a solution to the Wheeler-DeWitt equation incorporating contributions from all genera. Furthermore, we demonstrate that the same Wheeler-DeWitt equation can also be derived through the stochastic quantization.
28 pages, 3 figures; v2: corresponds to the version accepted in Phys. Rev. D
References in corpus (15)
- 2d CDT is 2d Horava-Lifshitz quantum gravity
- A String Field Theory based on Causal Dynamical Triangulations
- A Matrix Model for 2D Quantum Gravity defined by Causal Dynamical Triangulations
- Loops versus Matrices - The nonperturbative aspects of noncritical string
- On the spectral dimension of causal triangulations
- A new continuum limit of matrix models
- Putting a cap on causality violations in CDT
- Trees and spatial topology change in CDT
- Stochastic quantization and the role of time in quantum gravity
- Summing over all Topologies in CDT String Field Theory
- Causal Dynamical Triangulation with Extended Interactions in 1+1 Dimensions
- Scale-dependent Hausdorff dimensions in 2d gravity
- Wormholes in 2d Horava-Lifshitz quantum gravity
- Criticality at absolute zero from Ising model on two-dimensional dynamical triangulations
- Towards elucidation of zero-temperature criticality of Ising model on 2d DT